It has previously been proposed to provide for damping of cylinders in printing machines as the cylinders roll off against each other and portions formed with grooves therein meet each other. Shocks will arise which result in bending oscillations of the printing machine cylinders. The damping system described in the referenced U.S. Pat. No. 4,125,073 is intended to reduce the amplitude of these bending oscillations so that they will attenuate rapidly. In accordance with the proposal, a ball fitted within a slit is eccentrically positioned in the cylinder. The ball, due to centrifugal force, will engage the inner wall of the cylinder. The ball is accelerated in the direction of the central axis of the cylinder due to the impact or shock to which the cylinder is subjected just after the groove has rolled off against an engaging cylinder. As the cylinder continues to rotate, centrifugal force again causes the ball to engage the inner wall of the cylinder. This occurs in advance of completion of the revolution of the cylinder, that is, in advance of the next roll-off event of the groove of the cylinder against an adjacent cylinder. It has been found that such an arrangement causes disturbances within the cylinder.